PyTorch Tutorial.ipynb

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  "metadata": {
    "colab": {
      "name": "PyTorch Tutorial.ipynb",
      "version": "0.3.2",
      "provenance": [],
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      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/smlra-kjsce/ML-DL101/blob/master/PyTorch%20Tutorial.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ov1iAF2VS5ks",
        "colab_type": "text"
      },
      "source": [
        "#PyTorch Tutorial\n",
        "<ol>\n",
        "<li><a href=\"https://pytorch.org/\">What is PyTorch?</a></li>\n",
        "<li><a href=\"https://pytorch.org/tutorials/\">What can we do with it?</a></li>\n",
        "<li><a href=\"https://www.google.com/url?sa=i&source=imgres&cd=&cad=rja&uact=8&ved=2ahUKEwjBsLzk6LTkAhXFfn0KHeZRApgQjRx6BAgBEAQ&url=https%3A%2F%2Fblog.algorithmia.com%2Fexploring-the-deep-learning-framework-pytorch%2F&psig=AOvVaw3eLYpoGyGHRVB5KUBSwjIN&ust=1567605789915136\">What is a Computation Graph?</a></li>\n",
        "<li>Looking at a detailed example of PyTorch Graph.</li>  \n",
        "</ol>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8B7ImskqdjGJ",
        "colab_type": "text"
      },
      "source": [
        "##Installing PyTorch"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kavThgwUZHXN",
        "colab_type": "code",
        "outputId": "ca33f506-6697-436f-d51f-a2c4cde9e677",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 367
        }
      },
      "source": [
        "!pip3 install torch torchvision\n",
        "!pip3 install torchviz"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: torch in /usr/local/lib/python3.6/dist-packages (1.1.0)\n",
            "Requirement already satisfied: torchvision in /usr/local/lib/python3.6/dist-packages (0.3.0)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from torch) (1.16.5)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from torchvision) (1.12.0)\n",
            "Requirement already satisfied: pillow>=4.1.1 in /usr/local/lib/python3.6/dist-packages (from torchvision) (4.3.0)\n",
            "Requirement already satisfied: olefile in /usr/local/lib/python3.6/dist-packages (from pillow>=4.1.1->torchvision) (0.46)\n",
            "Collecting torchviz\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/8f/8e/a9630c7786b846d08b47714dd363a051f5e37b4ea0e534460d8cdfc1644b/torchviz-0.0.1.tar.gz (41kB)\n",
            "\u001b[K     |████████████████████████████████| 51kB 3.9MB/s \n",
            "\u001b[?25hRequirement already satisfied: torch in /usr/local/lib/python3.6/dist-packages (from torchviz) (1.1.0)\n",
            "Requirement already satisfied: graphviz in /usr/local/lib/python3.6/dist-packages (from torchviz) (0.10.1)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from torch->torchviz) (1.16.5)\n",
            "Building wheels for collected packages: torchviz\n",
            "  Building wheel for torchviz (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for torchviz: filename=torchviz-0.0.1-cp36-none-any.whl size=3520 sha256=12f353c1da7ce6b520a4b9e2d1fe0ec0a2b3f1048822dca9c27dc0a3b67648e0\n",
            "  Stored in directory: /root/.cache/pip/wheels/2a/c2/c5/b8b4d0f7992c735f6db5bfa3c5f354cf36502037ca2b585667\n",
            "Successfully built torchviz\n",
            "Installing collected packages: torchviz\n",
            "Successfully installed torchviz-0.0.1\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wzvrnoaRdvgp",
        "colab_type": "text"
      },
      "source": [
        "##Importing all Libraries"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qXfCVDrogpYq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import torch\n",
        "from torch.autograd import Variable\n",
        "from math import pi\n",
        "from copy import deepcopy\n",
        "import torchviz"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EW_u9hYHkA7C",
        "colab_type": "text"
      },
      "source": [
        "##Making Data\n",
        "##Formula: mx + b + A1sin(w1x+c1) + A2sin(w2x+c2)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m9UDNCd_jo80",
        "colab_type": "code",
        "outputId": "7b2d19f2-f559-4d4b-c350-08dc50bcf778",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 269
        }
      },
      "source": [
        "x = np.array([_/100 for _ in range(1000)])\n",
        "y = 4.5*x + 3 + 2.8 * np.sin( 2.5 * x + pi/3) - 5.2 * np.sin(5 * x + pi/5) + np.random.normal(size=1000)\n",
        "\n",
        "\n",
        "plt.plot(x,y)\n",
        "x = Variable(torch.tensor(x,dtype=torch.double))\n",
        "y= Variable(torch.tensor(y,dtype=torch.double))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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RFdDPVtVbtnMzEnV5RkOTY8mjQX/+2uX5dU5WlSZyQRER6SCiAvrH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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aqmgWMJvnxYV",
        "colab_type": "text"
      },
      "source": [
        "##How to compute a function in PyTorch\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QG2JAGkUm5z9",
        "colab_type": "code",
        "outputId": "eee48701-7d87-4977-9620-21bc770d018a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "m = Variable(torch.tensor(1.2,dtype=torch.double),requires_grad=True)\n",
        "b = Variable(torch.tensor(2.8,dtype=torch.double),requires_grad=True)\n",
        "A1 = Variable(torch.tensor(0.6,dtype=torch.double),requires_grad=True)\n",
        "w1 = Variable(torch.tensor(2.2,dtype=torch.double),requires_grad=True)\n",
        "c1 = Variable(torch.tensor(pi/4,dtype=torch.double),requires_grad=True)\n",
        "A2 = Variable(torch.tensor(-1.0,dtype=torch.double),requires_grad=True)\n",
        "w2 = Variable(torch.tensor(4.0,dtype=torch.double),requires_grad=True)\n",
        "c2 = Variable(torch.tensor(pi/3,dtype=torch.double),requires_grad=True)\n",
        "print(m)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor(1.2000, dtype=torch.float64, requires_grad=True)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AEQ75Ph0o8Ml",
        "colab_type": "code",
        "outputId": "49fa07e9-1b1a-4dcc-c9a9-b9a575569fdf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        }
      },
      "source": [
        "Y = m*x+b+A1*torch.sin(w1*x+c1)+A2*torch.sin(w2*x+c2)\n",
        "plt.plot(x.detach().numpy(),Y.detach().numpy())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f0ae2c72630>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3No83V+fw5KJsAMJCDGN7t+ep64dpLxSRFsajQDfGxAOzgcGABW611q5wojBp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\nTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BpG5ftm4q2K6",
        "colab_type": "text"
      },
      "source": [
        "##Optimization in PyTorch"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ecp9byoBsPkN",
        "colab_type": "text"
      },
      "source": [
        "###Initialization"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pwWRtShPqOfj",
        "colab_type": "code",
        "outputId": "e455c3b2-c2f2-4c7b-869b-5aa9d52640b7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "params = [0]*8\n",
        "params[0] = m = Variable(torch.tensor(1.2,dtype=torch.double),requires_grad=True)\n",
        "params[1] = b = Variable(torch.tensor(2.8,dtype=torch.double),requires_grad=True)\n",
        "params[2] = A1 = Variable(torch.tensor(0.6,dtype=torch.double),requires_grad=True)\n",
        "params[3] = w1 = Variable(torch.tensor(2.2,dtype=torch.double),requires_grad=True)\n",
        "params[4] = c1 = Variable(torch.tensor(pi/4,dtype=torch.double),requires_grad=True)\n",
        "params[5] = A2 = Variable(torch.tensor(-1.0,dtype=torch.double),requires_grad=True)\n",
        "params[6] = w2 = Variable(torch.tensor(4.0,dtype=torch.double),requires_grad=True)\n",
        "params[7] = c2 = Variable(torch.tensor(pi/3,dtype=torch.double),requires_grad=True)\n",
        "print(params[0])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor(1.2000, dtype=torch.float64, requires_grad=True)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NwHY-8Q2qX6w",
        "colab_type": "code",
        "outputId": "69bbb7e5-8ba1-4e84-ea1d-0ae8a5d3a574",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        }
      },
      "source": [
        "Y = params[0]*x+params[1]+params[2]*torch.sin(params[3]*x+params[4])+params[5]*torch.sin(params[6]*x+params[7])\n",
        "plt.plot(x.detach().numpy(),Y.detach().numpy())\n",
        "plt.plot(x.detach().numpy(),y.detach().numpy())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1cee40e5f8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RtNDbKnem2jcthgX2Qxs9sXU+fDYLMod7d70r8V2Nvv0BF3p3fUNt82MRsb7V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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lvNX2f4ksUBB",
        "colab_type": "text"
      },
      "source": [
        "###Computing the Loss and Gradients!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KrascydGKaMn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Initialize\n",
        "\n",
        "params = [0]*8\n",
        "params[0] = m = Variable(torch.tensor(1.2,dtype=torch.double),requires_grad=True)\n",
        "params[1] = b = Variable(torch.tensor(2.8,dtype=torch.double),requires_grad=True)\n",
        "params[2] = A1 = Variable(torch.tensor(0.6,dtype=torch.double),requires_grad=True)\n",
        "params[3] = w1 = Variable(torch.tensor(2.2,dtype=torch.double),requires_grad=True)\n",
        "params[4] = c1 = Variable(torch.tensor(pi/4,dtype=torch.double),requires_grad=True)\n",
        "params[5] = A2 = Variable(torch.tensor(-1.0,dtype=torch.double),requires_grad=True)\n",
        "params[6] = w2 = Variable(torch.tensor(4.0,dtype=torch.double),requires_grad=True)\n",
        "params[7] = c2 = Variable(torch.tensor(pi/3,dtype=torch.double),requires_grad=True)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YKCEQTGOqmZB",
        "colab_type": "code",
        "outputId": "db21795e-5fa9-4a6a-ee3d-ff144cccee76",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 255
        }
      },
      "source": [
        "# Compute the function\n",
        "Y = params[0]*x+params[1]+params[2]*torch.sin(params[3]*x+params[4])+params[5]*torch.sin(params[6]*x+params[7])\n",
        "\n",
        "# Compute the loss\n",
        "loss = ((Y-y)*(Y-y))/2\n",
        "loss = loss.sum()\n",
        "print(loss)\n",
        "\n",
        "# Zero out the gradients\n",
        "for i in params:\n",
        "  if i.grad!=None:\n",
        "    i.grad.data=torch.tensor(0.0,dtype=torch.double)\n",
        "\n",
        "# Compute Gradients\n",
        "loss.backward()\n",
        "for i in params:\n",
        "  print(i.grad)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-1-2543d7749c64>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mY\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mparams\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m7\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;31m# Compute the loss\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mloss\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mY\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mY\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mloss\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mloss\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'params' is not defined"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jo8Kv8bF-fXX",
        "colab_type": "text"
      },
      "source": [
        "###Updating the parameters"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZC_QPP0D-ebU",
        "colab_type": "code",
        "outputId": "20e5136f-2e0d-4176-a9a6-9edad7ef13a4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 207
        }
      },
      "source": [
        "# Update Paramters\n",
        "lr = 1e-5\n",
        "for i in range(len(params)):\n",
        "  params[i] = Variable(torch.tensor(params[i] - lr*params[i].grad.data,dtype=torch.double),requires_grad=True)\n",
        "\n",
        "for i in params:\n",
        "  print(i)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor(2.3147, dtype=torch.float64, requires_grad=True)\n",
            "tensor(2.9671, dtype=torch.float64, requires_grad=True)\n",
            "tensor(0.6043, dtype=torch.float64, requires_grad=True)\n",
            "tensor(2.1470, dtype=torch.float64, requires_grad=True)\n",
            "tensor(0.7826, dtype=torch.float64, requires_grad=True)\n",
            "tensor(-0.9869, dtype=torch.float64, requires_grad=True)\n",
            "tensor(4.0582, dtype=torch.float64, requires_grad=True)\n",
            "tensor(1.0562, dtype=torch.float64, requires_grad=True)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:3: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n",
            "  This is separate from the ipykernel package so we can avoid doing imports until\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nSkTXLFJLNDW",
        "colab_type": "text"
      },
      "source": [
        "##Complete Training Loop"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lEIGtSH0LMT3",
        "colab_type": "code",
        "outputId": "dd658b3a-eedc-47c0-aa4f-66d197697821",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "losses = []\n",
        "\n",
        "x = np.array([_/100 for _ in range(1000)])\n",
        "y = 4.5*x + 3 + 2.8 * np.sin(0.5 * pi * x + pi/3) - 5.2 * np.sin(0.25 * pi * x + pi/5) + np.random.normal(size=1000)\n",
        "\n",
        "\n",
        "plt.plot(x,y)\n",
        "x = Variable(torch.tensor(x,dtype=torch.double))\n",
        "y= Variable(torch.tensor(y,dtype=torch.double))\n",
        "\n",
        "params = [0]*8\n",
        "params[0] = m = Variable(torch.tensor(5,dtype=torch.double),requires_grad=True)\n",
        "params[1] = b = Variable(torch.tensor(0,dtype=torch.double),requires_grad=True)\n",
        "params[2] = A1 = Variable(torch.tensor(2.7,dtype=torch.double),requires_grad=True)\n",
        "params[3] = w1 = Variable(torch.tensor(0.9*pi,dtype=torch.double),requires_grad=True)\n",
        "params[4] = c1 = Variable(torch.tensor(1.1*pi/3,dtype=torch.double),requires_grad=True)\n",
        "params[5] = A2 = Variable(torch.tensor(-5.0,dtype=torch.double),requires_grad=True)\n",
        "params[6] = w2 = Variable(torch.tensor(0.23*pi,dtype=torch.double),requires_grad=True)\n",
        "params[7] = c2 = Variable(torch.tensor(0.9*pi/5,dtype=torch.double),requires_grad=True)\n",
        "\n",
        "lr = 1e-3\n",
        "\n",
        "for epoch in range(100001):\n",
        "  \n",
        "  # Learning Rate Scheduling\n",
        "  #lr = lr*0.99\n",
        "  \n",
        "  # Compute the function\n",
        "  Y = params[0]*x+params[1]+params[2]*torch.sin(params[3]*x+params[4])+params[5]*torch.sin(params[6]*x+params[7])\n",
        "\n",
        "  # Compute the loss\n",
        "  loss = ((Y-y)*(Y-y))/2\n",
        "  loss = loss.sum()\n",
        "\n",
        "  # Zero out the gradients\n",
        "  for i in params:\n",
        "    if i.grad!=None:\n",
        "      i.grad.data=torch.tensor(0.0,dtype=torch.double)\n",
        "\n",
        "  # Compute Gradients\n",
        "  loss.backward()\n",
        "  # for i in params:\n",
        "    # print(i.grad)\n",
        "  \n",
        "  losses.append(loss.detach().numpy())\n",
        "    \n",
        "  # Update Parameters\n",
        "  for i in range(len(params)):\n",
        "    params[i] = Variable(torch.tensor(params[i] - lr*params[i].grad.data,dtype=torch.double),requires_grad=True)\n",
        "  \n",
        "  if epoch%10000==0:\n",
        "    print('Epoch: ',epoch)\n",
        "    print(\"Loss: \",loss)\n",
        "    plt.plot(x.detach().numpy(),Y.detach().numpy())\n",
        "    plt.plot(x.detach().numpy(),y.detach().numpy())\n",
        "    plt.show()\n",
        "    \n",
        "for i in params:\n",
        "  print(i)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:49: UserWarning: To copy construct from a tensor, it is recommended to use sourceTensor.clone().detach() or sourceTensor.clone().detach().requires_grad_(True), rather than torch.tensor(sourceTensor).\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch:  0\n",
            "Loss:  tensor(7042.9711, dtype=torch.float64, grad_fn=<SumBackward0>)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PzGNvMnLxPQBM/HWy23qRNa6lTJCxkpDSWboiRu+HTdMhchxUaujzeIUoKSSh\ni0J3PtEYJGQ1xQCw4/x2x7Hqpsw5wq+v34zwIDdLw618FQJCZWi/EFeQhC4K3fmkOGNDG79+tcpk\nTi9rz7K+ZkRIGGGBlxN6RrPKsX9g72Lo8jiEVSqMcIUoMaSXiyhU647v44E/h2XsmbDb7eyP2+U4\nbtPpfND5exLTjPVALcpI+kqbjUUlVr4K4dWhw0OFHboQxZ4kdFGoJm2cm7ljTuD670Zzka2OIqu2\n0rthC8d+kyq1uDZkEA+0uR2Orobj/0D/dyEwtDDDFqJEkIQuCpX9ijU5sybzQFttnu38uNNxk8nE\n7GGvGzvf3GQ8nbca5fM4hSiJJKGLQmXT7rsoAmwauzT7E4+ugWNroN9bEBDsg8iEKPnkpagoVDZt\nzd+Jf70FYVWgzWjvBiSEH5GELgqVPZsn9Aq0zv6kY//AkVXQ+TEIcNONUQgBSEIXhexIwg6XMm0P\n5K/R07M/adU7EFoJIu/2YWRClHzShi58bueZ4+yNNob5p5qPuhy/q8HT2Z98ZiccWgk9X4DAMB9F\nKIR/kIQufG74sltRplTGNHjF5ViYvTETuw1zPemyfz6FgDBjmL8QIkfS5CK8zmqz8faq2VhtRhdF\nZUo1fuI6idaV3RidxJ2EHXOg9SgIreCTWIXwJ5LQhdc9t2IK3x35L8+tmOJU/s3+Nx3bD137FgCB\nphxecm74ErQdOjzokziF8DfS5CK87sSlKAB+ifqOZdM/yTxgTnFs3h/Zj+1n9zKh4wj3F0m5BBu/\nMZaVK1/Ph9EK4T8koQuvs2U0o2jLxWzrmEwmJg2ckP1FNn8LqZeg0yPeDk8IvyVNLsLrDiVsK9gF\nbOmwbhLU7QI123gnKCFKAUnowqsW7F5HmvlYjnUeaJzLgs67FsClKHk6FyKPpMlFeNXF5IRsj2lt\nZvtdmzGZcniO0BrWfgyVroZGN/ggQiH8lzyhC68KD85hWlttyTmZgzHE/8x26PgfyK2uEMKJPKGL\nApu742/m7F3GkfidVA9pkEPN7GdadFj7iTEJ13W3ey0+IUoLSeiiwF7d/ICxYYbDaYecjmltQqmM\nRK5ySejn9sDB36DHCzJFrhD5IH/TCp+opNoaGzrzV0ypHEaFgjHM3xICbWWYvxD5IQld+ESw+fJE\nWq7D/d2KPwvbZ0OrO2WYvxD5JAld5MuqI7t4468fAdDaNWmHmI2Xo8qU7tkFN0w2+p/L4s9C5Fuu\nCV0pVVsp9YdSardSapdS6rGM8gpKqd+UUgcyfpb3fbiiuHh41XB+PHq5P7lrQq8WVs2l7NZaT7q/\nWFoibJwC19wEFXN6qSqEyImtujiMAAAZpElEQVQnT+hW4AmtdROgA/CwUqoJ8AywUmvdCFiZsS9K\nIeXmZeeIZn1dyl7tlc3ycVtnQHKs0VVRCJFvuSZ0rfVprfXmjO14YA9QExgMXF5mZjpws6+CFMWX\n3e6+50pIQCDf3fAz3/Saj8VaneZht2RzARus+xxqRkKdDj6MVAj/l6dui0qpekArYD1QVWt9OuPQ\nGaCqVyMTJUKazYrJWhG75YJTebAlkGbV6gCwZdyv2V9g31KIOQxDXwLl4QtUIYRbHr8UVUqVAX4C\nHtdaX8p6TGutAZ3NefcppTYqpTZGR0cXKFhRtC4kxTN2wZukpKc5ypLT0whQZV3qhgQEenbRtZ9C\nRB24ZqC3whSi1PIooSulAjCS+Q9a63kZxWeVUtUzjlcHzrk7V2s9WWsdqbWOrFy5sjdiFkXkvp9f\n59+4Gby1epajLDE9DZtOc6kbZPEgoUdthBPrjJ4tZhnjJkRBedLLRQFTgD1a6/ezHFoEXH7LNRpY\n6P3wRHGSkG78YZZmy+yK+Nqqb7BaTrrUDTCbc7/gmg8guBy0Gum1GIUozTx5LOoMjAJ2KKW2ZpQ9\nB/wPmK2UGgccA3JY6Vf4A62NF6BWe+aIz79jpjnVGd/0Pc4kXqBqmXI5X+zcHti7GLpNhKBwb4cq\nRKmUa0LXWq8h++F+vbwbjijObBiJ/JeoH7L9zbmlSSfKh5bJ/WJrPoCAMFkvVAgvkpGiwmN2bTV+\nXtGjJSuPknnMEdgxFyLvlmH+QniRJHThkdikBC5Zz2Z7PNTeiDW3r/fsYn9/CCazDCQSwsskoQuP\nDJh9L2nmE9keDzGVo1xOi1tcdumUMTK01UgoW92LEQohpK+Y8MgltTPbY23L3cFL3Tyc8vbvj43R\noZ0e9VJkQojLJKGLAps8cCIWT7opXjxhTMLVcgRUqO/7wIQoZaTJRRSYR8kcYNXbxs/rn/ZdMEKU\nYpLQReG4cAi2/ABt7jaG+gshvE4SusgTZY0gQrfI+4l/vAGWIOj6hPeDEkIAktBFLux2Oz/v+Tez\nQGkWDJvEWx2meX6Rk5tg51xo/wCEy6ScQviKvBQVQOa85iaT83d8h2m3kWw+4NivFticiqHh9G/c\nhnTb1xyOPZXzhbWGZc9AWBXoMt7rcQshMklCFwC0/KY7KM32saudyrMmc4BJN77s2B7cpH3uF94x\nF6I2wKBPIdh1ml0hhPdIk4sAQFti0eaLALy35id2nXUdRNSu3J00qOi6Vmi2UhNgxctQvQW0vNNb\noQohsiEJXThJSk9l2qFXuHPxGKeFLACm3JzHZWN/fw0unYQb3waT/KoJ4Wvyf5lwcj7RmPPcZjnH\nbXMmOsrvbvBq3i50YgOs/wLa3itrhQpRSCShCyfnEuIc28fSVzq2VV7W+7SmwsL/QNma0Pvl3OsL\nIbxCXooKJ+eTLrktb171Ks8vsuIVOL8P7pwri1cIUYjkCV04iU2Odym7s/4L9G7o4WCifctg3efQ\n7n5o1MfL0QkhciIJXTi9/IxJdn1Cb1mtkWcXijkMCx6EatfBDf/1VnhCCA9JQhfEpSY7tpcc+tXl\neNkgD+Y5T46FHzKWlR06zRjmL4QoVJLQS7FP/llIdMIlktNSHWUnrH+61CsfksuycmlJMGsUxB6F\n23+Aig28G6gQwiOS0Eup9ccPMHn/Cwyb9zjJ1jSX4483fdexneNKRGmJMGMYHPsbbvkC6nX2RbhC\nCA9IQi+lVh7ZCEBs+jFSrOkux0e17OXYjggJc3+R+LPw7c0ZyXwyNL/NJ7EKITwj3RZLqR+PvgGA\nHSvJ6akuxwMtmb8aoQFu2sNPbIDZo42286HToMlgX4UqhPCQJPRSTltiSHKT0AGwhYP5im6MKXHw\nx5vGKNBytWHcr1D9Ot8HKoTIlSR0wen4C077yloBgDkDZ7PzzDGj8NIp2DQd1k8yknrbe6DXyzKD\nohDFiCR0weHYk077NYKaQOwxrok/yjUx62Ham3B0DaCh8U1w/USo0bJoghVCZEsSeimSlJ7K4Qtn\nSUq66FQ+98TbTvvtL/4CH83I2FNQtZmxsPN1w6RLohDFmCT00sBuhxPrefa3l/g94Eyu1c8EN4ZB\ndxiTa9VsDSHlCyFIIURBSUL3U1abjY7TB/JweEPGnPoLYo9yqGYNcvpPHmZvTKJpH6fDmkDruwov\nWCGEV0g/dH+kNQnb55JiPsFnCSshrDLcMplzppxnTAy3VATApMyFEaUQwsvkCd3fpMTBokcx71kI\n9WqTRiCM+w2UwrJ5fo6nhlrKQBrUCKtRSMEKIbxJEro/id4HPw6H2GPEd5wAp+dg1xbIWJwiyBxK\nvM7+9P4NenEptSOPdby5kAIWQniTNLn4i6hNMLUvpCaQMmo+4+My5mcxp7Dp5CEAgs3OQ/gDbLWd\n9ns3aM1TXW9zGiUqhCg5JKH7g+PrYfpACC4H45Yzcc92dictdBwes8J44tba7nRahYBaju1to7bR\noGK1wolXCOETuSZ0pdRUpdQ5pdTOLGUVlFK/KaUOZPyUfm1F5ewumDEUwqvC2OVQ4Sqik6LdVrVq\n50m47FkSvMkk3+1ClHSe/F88Deh3RdkzwEqtdSNgZca+KGyXTsP3QyAgFEYtgHDjCTvFluJS9c/D\nOzmXvhts4fSp8hAAGjsTr/uIduVGFmrYQgjfyLWxVGu9SilV74riwUD3jO3pwJ/A016MS+TGmgZz\nRkPKJWOCrPJ1HYfS7K4J/ZHVI8BstJtXCo0AjCaYUa16MqpVz0ILWwjhO/n9O7uq1vp0xvYZoGp2\nFZVS9ymlNiqlNkZHu28KEPnwyzNwYj0M/hSqNXM6lGbLZvZEwISFGxq0BaBLzet9GqIQonAVuDuD\n1lorpbLtDKe1ngxMBoiMjMyh05zw2K75sHEKdHoUmt0KgN1u55cDW+jfuA1W7boC0WUBKpjIWg3Z\nMnIrFrMMIBLCn+Q3oZ9VSlXXWp9WSlUHznkzKJGDS6dh8Xio2QZ6veQofnfNXL478l+2nH4WrbP/\n3qxdphGAJHMh/FB+m1wWAaMztkcDC3OoK7xFa1j4MKSnGEu+mQMchy6mGgtRrDi+IsdL1Cojo0CF\n8FeedFv8EfgHaKyUilJKjQP+B/RRSh0AemfsC1/b8h0cWgk3/BcqNXQ6VCbQWMj5kjXn2RRDLCE+\nC08IUbQ86eUyIptDvbIpF76QEA2/vgh1OxurBV0h1Wq0m6dxAU3lbC8TEhDssxCFEEVLRpOUFL+9\nCGmJMOADx9wsYLwMHbvgTVafXG0UmJOIYbPTqVn7mZtlJkUh/JYk9JLgyCoO755D87rVmXb8hNOh\n3w5t49+4GUTr9dmePrHzKCIwloyzmCShC+GvJKEXd3YbLJ3IX2WNUaDz9i91HHpn9RyeXJv7QhTh\nQcGOeVwkoQvhv2RaveJu+yyI3sORxndC2mpMysyec1EMW3ajx5cIDwpBYyT0ALP8JxfCX8kTenGW\nngJ/vAE1WnM+o/+4QrH62I48XSYsIIiRTUYB0LdhpNfDFEIUD/K4Vky1nnojle0JLI87AYM/w75r\nIwAmZSLQFJDL2c5MJhMPtuvPg+36+yJUIUQxIU/oxVS6OYpTARehQU+46npsdqPJ5HTSEVaf2JT9\nibbQQopQCFHcSEIv5tJ6vACAXdsAiDftZkPc9051/nPtW1n2FEKI0qnUJ/R90adoN/UW9kZHFXUo\nmeLPOjbbrBzDj9v+wpaR0N25v11/GgX1B1sZJKELUXqV+oT++uqpJJsP8vqqqU7lS/ZtZPmBLUUS\n06z5jzjtf7T5U+xuJtz6X4dveLH1JADmDX+LHWP/Ydw1xrT045u+5/tAhRDFirwUzaBxTpjPrLsb\ngL6N8tajpMAuHOI1vcepKNG0l/1xuHz93tTYtcfK451u5vFOxhqiH+zyVZBCiOKo1D+hq4wmiisT\nel7sOnuC99b8lKdztp85Sr/vH+b534y/DFLS09h6+ihvzbvXbf0kx3oihgBrLbf1siqnmxNgq52n\nuIQQJZdfP6FbbTaGznmWCe3H0LV+E7d1Lk+LksMU4rm6c/EYbJZzPNx+IMEBgR6d8/AvL3BRbePk\nqVU8nnAboxc+zwnrn5DN6doc57T/Vb9Pc73HmjEzPIpFCOEf/PIJPT41mRFzXmLe7n84mLqMR38f\n79P7Wc3G0nqJ6c5Lvz3z61f8G3XQ7TmxOrM9pOdPnY1kngdtajbIW5BCCL/nNwn9vTU/8fOefwF4\n+fep7EyazyebvsjxnH3Rp7K8bLQXOIboxDi+2fQbYHypLDn9MeOWG23xfb57wNEsE5eShDJZ832f\nzhXGFDhWIYT/KdEJ/c/DO2kxpQcHzp9m2qFXeG7DWAAS0pMAsOn0bM89GnOO25b2ZUv8LAB2JM53\nW+++Re/kGMOhC2e4vKTqg8te4v2dE1iybyNzd64BwG5KwG63c8b+N9MOvcLyA1voMeO2vH3QK3wx\n8IkCnS+E8E8lOqG//c+X2C3nmbxpkVO5zW702Vbq8sdz7Zt9PulSttcdNud5x/Y/sd/yxC+TuHfh\nO9jtmU/xQ2Y9Q/PpzRmz+KnMa1r3AnApJZH3d07IKDURm5LoqPPk2rtINztPgetOhwjnWRTvu/o1\nALQ9b8P+hRClR4l8KXo45iyzd/6JJWNOk8S0JKfj1oyErrUGBVbLSQDOJsTRZ9ZAnmj1Mo0rufYS\niU1K4J6fX2N/yhKn8l/Pfg7AZ+uvpnnVBkzftshRJ8kWAxkz0mpTEgoIzbIqkMLE+cT4PH/G+9rc\nwrqV3zr2H+k4mHoRNbiqQrU8X0sIUTqUyIQ+YuGDJJkOUMXUAYCYlBin4zZttE/rLO3ipy7FsPbY\nHrQllnd3PI7ZWs3l03eb0zHH+07e/wLsdy6z6zTHtlLGF8nUbbMzK2jFhRz+GshO21oN+X3I39z6\n08O0r9oZgIHXts3zdYQQpUeJTOjJOtppPy7tomP7g7/nY7UbCT1dZz65742OQpkym15slpwXU/aU\n1c11Dqf9mrljTmbrGfc9XXJTuUxZVo/+Lr+hCSFKmRKV0DedPMS204cc+xaV0eRizXwCnnrwJcd2\nqvmYY3tP9DGCLZ71Efe2SXufLZL7CiFKlxKR0BNTU7lp5gNcwJgTXBEBwCmbsTBymj0x19e7609t\no0WVa30aZ169cz4BW7mGPBPgnb8WhBClW4no5bLtzBFHMjc4D+tMtSfkeo0t8bNYe/LfAsdSw9y1\nwNe4rF98LDcN/BCLtaZT+ZDaT2VzhhBCZK9EJPQzCbFO+1cOg7/ci+XyzIPZubL3CsCrkZNpWWaY\nx7GUCyzvUlZWN/f4/MvuvpgALe+Aqk2ZOch5pscH2g7M8/WEEKJEJPSjsadzrwSUCQxx2g+x5T48\n3m63Uzm0klNZZNkR2dfP0nOmrG4GQM9aN3gUX1Z3JSZDD6O/e2hAkNOxomrrF0KUbCUioX9z6GWP\n6pUJDHbaXzdmntt65fR1ju1rKtcmNsX4CyDAVosXW0/i7paDs71H1sFFv905jXsbvcajHW7Ntn52\nTTSq1VgoZzS1VAgp43TsygQvhBCeKBEJvbJq71G9sCsSuslkIsBai1D71fw+5G+uDR3E591m0axi\nawAGVn+cZtXqEJtqJPTeNW9hWPMudKpzDUG2+m7vkfUJPTQgiEc7DaZiaBm3dd/t9C3LR37u2P/y\n+sz+6cGdH8+MOyiIHaN3oLUxQinQUiLeVQshipkSkTkWj/iMbt8NceqG6E7WJperAo1mkM3jljnK\nZg99HYA2tRrw4doaPNP1dgDe6jWeiSvsPH/9SAAsZjMbxy7i03U/8+W+55zuobXrJF4mk+v34tz+\ny2lcuQYAXSuMZX30SjqlRxGgNelKEVKmkss5H3aZzs/7V+f4GYUQIjslIqGHBgQ5PRlnp1xwZkJf\nOCL7JdhCA4J47vrMdvLGlWu4rf+fDgP5ct9zKGsE2mIMXrJjZ/aNyxzzqGdVVjejZthVPNhmuCOZ\nA3w+cDxYH4LPOzJDm5ly9X1uvwR6N2xB74Ytcv2cQgjhTolI6AARlhpEa/eTWilbObQ5jrLBoV6/\n75LBv7Pl1GFe+PceAOzazrVVXOeB+feOTVhMZixms/sL/fMpxBzimpE/8U7D3l6PUwghSkxC/+m2\nD7Oda+XXoT/zx+HthAYEMb7pe1i1zWv3rRNRmcMxZx37LSpd57ZejisVXTwBq96FawaAJHMhhI+U\nmIRePrQMD137Fp/vedpRdnXwTQSaAqkWXp4RLa4HYGxk3rsQ5saU0b6itYnXet+d9wv8+jxoO/R9\nw8uRCSFEphKT0AHGtb7BkdB3jN5RaPdNSEsBINhe123bd452L4LdC6HnC1C+rg+iE0IIQ4G6LSql\n+iml9imlDiqlnvFWUNkJtFjAFlboS7Dd0LAljUMG8FW/j/J2YuIFWDIBqreALN0UhRDCF/L9hK6U\nMgOfAX2AKOBfpdQirfVubwXnzo6x64yN+DNwfB2c2wPJMYCC0IpQtQnUjISy1b12T4vZzNxhb+b9\nxGVPQfJFGLUAzLLSkBDCtwrS5NIOOKi1PgyglJoJDAZ8l9DtdtizCDZMhmNrMSbpUhBc1thMzTLH\nS8020Ow2aHUnBJfzWUjZ2vID7PzJGN5frVnh318IUeoUJKHXBLL2I4wCPBvSmR/H18Pi8XBuF5Sv\nDz2eM3qMVG0Kloyh8unJcHYXHF0NuxbA8mfhjzegzWjoMgHCKvosPCfn9sCSJ6BeV+gqCzoLIQqH\nz1+KKqXuA+4DqFOnTv4usuwZWP8FlK0JQ6ZA01vA5Ka/d0AI1Io0/ukyHk5uhn8+g3Wfw+bvoOsE\naP8ABAS7nustybEwaxQElYEhX7uPUwghfKAgL0VPArWz7NfKKHOitZ6stY7UWkdWrlw5f3cKiYAO\nD8LD66D5bZ4nyZqt4bYp8OBaqNMeVrwMn7U1ep1onfv5eWVNhZkj4eIxGDodwmVBZyFE4VE6n4lN\nKWXBWDK5F0Yi/xe4Q2u9K7tzIiMj9caNG7M77HuH/4RfnoVzu43mkH7/8177ti0dfroHdi+AW7+G\n64Z657pCiFJPKbVJax2ZW718P6Frra3Af4DlwB5gdk7JvFi4qjvcvxr6vwtnd8KXXY227qSYgl03\nPQXmjDGSed83JJkLIYpEvp/Q86PIn9CzSoqBP9+Ef6dAULjRGyVyLJjz+Foh7iTMGgmnNsONb0P7\n+30TrxCi1PL5E3qJF1oB+r8DD6wxBv4sewq+6AJ7l4Ldg7lg7DbYNB0mdYTz+2H4DEnmQogiVaKG\n/vtE1SZw10LYu8SYc2XmCChXG1qMgEZ9oEarzEFBWhsvPPctgw1fQcwhqNsFBn4ElRoW7ecQQpR6\npbfJxR1bOuxbajTDHF1tTKilzBBe3WiKSTwPaQlG3RqtjOH81w6CvM7vIoQQeeBpk4s8oWdlDoAm\ng41/kmLgyF/GQKW4KLBbIaQ8VLoaGvSEirkvQC2EEIVJEnp2QisYA5ia3lLUkQghhEekrUAIIfyE\nJHQhhPATktCFEMJPSEIXQgg/IQldCCH8hCR0IYTwE5LQhRDCT0hCF0IIP1GoQ/+VUtHAsXyeXgk4\n78VwSgL5zKWDfObSoSCfua7WOtcVggo1oReEUmqjJ3MZ+BP5zKWDfObSoTA+szS5CCGEn5CELoQQ\nfqIkJfTJRR1AEZDPXDrIZy4dfP6ZS0wbuhBCiJyVpCd0IYQQOSgRCV0p1U8ptU8pdVAp9UxRx+Nr\nSqnaSqk/lFK7lVK7lFKPFXVMhUEpZVZKbVFKLS7qWAqDUipCKTVXKbVXKbVHKdWxqGPyNaXU+Izf\n6Z1KqR+VUsFFHZMvKKWmKqXOKaV2ZimroJT6TSl1IONneW/ft9gndKWUGfgMuBFoAoxQSjUp2qh8\nzgo8obVuAnQAHi4FnxngMWBPUQdRiD4CftFaXwO0wM8/u1KqJvAoEKm1bgaYgeFFG5XPTAP6XVH2\nDLBSa90IWJmx71XFPqED7YCDWuvDWus0YCYwuIhj8imt9Wmt9eaM7XiM/9FrFm1UvqWUqgXcBHxd\n1LEUBqVUOaAbMAVAa52mtb5YtFEVCgsQopSyAKHAqSKOxye01quAmCuKBwPTM7anAzd7+74lIaHX\nBE5k2Y/Cz5NbVkqpekArYH3RRuJzHwITAXtRB1JI6gPRwDcZzUxfK6XCijooX9JanwTeBY4Dp4E4\nrfWvRRtVoaqqtT6dsX0GqOrtG5SEhF5qKaXKAD8Bj2utLxV1PL6ilBoAnNNabyrqWAqRBWgNTNJa\ntwIS8cGf4MVJRpvxYIwvsxpAmFJqZNFGVTS00b3Q610MS0JCPwnUzrJfK6PMrymlAjCS+Q9a63lF\nHY+PdQYGKaWOYjSp9VRKfV+0IflcFBCltb78l9dcjATvz3oDR7TW0VrrdGAe0KmIYypMZ5VS1QEy\nfp7z9g1KQkL/F2iklKqvlArEeImyqIhj8imllMJoW92jtX6/qOPxNa31s1rrWlrrehj/fX/XWvv1\nk5vW+gxwQinVOKOoF7C7CEMqDMeBDkqp0Izf8V74+YvgKywCRmdsjwYWevsGFm9f0Nu01lal1H+A\n5RhvxadqrXcVcVi+1hkYBexQSm3NKHtOa720CGMS3vcI8EPGg8ph4O4ijsentNbrlVJzgc0YPbm2\n4KcjRpVSPwLdgUpKqSjgZeB/wGyl1DiMWWeHef2+MlJUCCH8Q0lochFCCOEBSehCCOEnJKELIYSf\nkIQuhBB+QhK6EEL4CUnoQgjhJyShCyGEn5CELoQQfuL/AWbanuSc1iIUAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch:  10000\n",
            "Loss:  tensor(nan, dtype=torch.float64, grad_fn=<SumBackward0>)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch:  20000\n",
            "Loss:  tensor(nan, dtype=torch.float64, grad_fn=<SumBackward0>)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wFNDzxfolMLkjrJgdnL9xOfz7evjsmeif3X0M7HG8S2s3IpGCpYCeL7583R0/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\nKKCLiBQIBXQRkQKhgC4iUiD+H9MZQ6auhjQSAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch:  30000\n",
            "Loss:  tensor(nan, dtype=torch.float64, grad_fn=<SumBackward0>)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wFNDzxfolMLkjrJgdnL9xOfz7evjsmeif3X0M7HG8S2s3IpGCpYCeL7583R0/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\nKKCLiBQIBXQRkQKhgC4iUiD+H9MZQ6auhjQSAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch:  40000\n",
            "Loss:  tensor(nan, dtype=torch.float64, grad_fn=<SumBackward0>)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wFNDzxfolMLkjrJgdnL9xOfz7evjsmeif3X0M7HG8S2s3IpGCpYCeL7583R0/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\nKKCLiBQIBXQRkQKhgC4iUiD+H9MZQ6auhjQSAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch:  50000\n",
            "Loss:  tensor(nan, dtype=torch.float64, grad_fn=<SumBackward0>)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch:  60000\n",
            "Loss:  tensor(nan, dtype=torch.float64, grad_fn=<SumBackward0>)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wFNDzxfolMLkjrJgdnL9xOfz7evjsmeif3X0M7HG8S2s3IpGCpYCeL7583R0/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\nKKCLiBQIBXQRkQKhgC4iUiD+H9MZQ6auhjQSAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch:  70000\n",
            "Loss:  tensor(nan, dtype=torch.float64, grad_fn=<SumBackward0>)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wFNDzxfolMLkjrJgdnL9xOfz7evjsmeif3X0M7HG8S2s3IpGCpYCeL7583R0/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\nKKCLiBQIBXQRkQKhgC4iUiD+H9MZQ6auhjQSAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch:  80000\n",
            "Loss:  tensor(nan, dtype=torch.float64, grad_fn=<SumBackward0>)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wFNDzxfolMLkjrJgdnL9xOfz7evjsmeif3X0M7HG8S2s3IpGCpYCeL7583R0/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\nKKCLiBQIBXQRkQKhgC4iUiD+H9MZQ6auhjQSAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch:  90000\n",
            "Loss:  tensor(nan, dtype=torch.float64, grad_fn=<SumBackward0>)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wFNDzxfolMLkjrJgdnL9xOfz7evjsmeif3X0M7HG8S2s3IpGCpYCeL7583R0/\netTL+/oDuH1Y/M+WVbhp/qAWukgB03ro+cK/MmJJKTTUwbSfu6GKiSitDP68iBQktdDzhX8UiymB\npW8lHswByird7FBwOxKJSEFSCz1Xff0+lJRBn33c+XddJiVQ1syhhyWlMOpat8Vc7wS6aEQkL6mF\nnqvuOxruOcI7D2yhx1p8q3WXyPmlZdBn39TVT0Ryjlro+cIf0GfdASvnRC9nTGbqIyI5Ry30XLdh\nmTsGbhe3fFZwmck1mauPiOQsBfRvv4Lre8A3X2a7JpHdPgw+f8lNIIrllPtgxI8BtdBFipUC+idP\nQmNt+KiR6i+yF+S/eDX4/KNHvJeigX7xCVzykUsPHQ8n3AYTH4HKjnDB2+mvp4jkFPWhR+tzvnM/\nd8xGd8ajE4LPF/xf5E0rOg8Iz+s/Eq5Znp56iUhOUwv9uy6KOF0asTTUwea1zftM/Q43+3P94uD8\nrz+IXH79kuDzjv3iP6NNt+bVSUTyWuG30FfMhp5Dou/Ok4pRIc/9FD59Gn67PvGZmK/+Bj64x6V/\nvRYWz4THJkYvv/6r4PNxd8Z/xmWfxd69SEQKSuG20Gu3QM0KuPdImH5p/PLxXjrG8qlvYSz/EraJ\nWDffS3/8WOxgHskuh8cvU94KKto0774ikrcKM6B//QH8sY974Qmw6qMYhVPQ5eLXWOulm5rc6oiv\nT3bnm1Z7/eDWwrJ3vLKJfOGIiMSR/wF923p3vPswePU6l/76v+64+A13jNat8uG/YGu1S29pZh94\nJOsXw/MXuT71Bl/wnuXrGvnLIHj0NJde+1lyz7liUXKfF5GClN8Bfd5TcPPOsPJDWP0xvOvbILmp\nwR2/68+OENA3fg3TLob373bncx+O/Ix/nRQ5v26rm/Sz+mO+a90//RN3n+Wz4P0pvkeXepOClrzp\nrv/z4Ob8lk7nKi/drkfzPy8iBS+/A/qSt9xxdUiXynezKn2BPGILPUYXy9/28dKLZ8LzP4enfgyN\nDV7+YxPdpJ9pl3h5231/LZS38bpaSkpd8Pd7/qLozw30o5eCz8+e5o5990/s8yJSdPJzlMuWahdo\nSyvceWDABK+F7h/hsfZTd9y23rXoJz4K3QeF37duK7x8TfiIkrkPueP3fgBddnZ/Gfi/TAK/LLZv\ndMfAfTtNKdRva97vB9Bl1+DzzgPg6q/dUrgiIhHkZ0B//HRY8T4MGe/O/f3ofqEBHWBHjTfm+/HT\nod/I8PveuFPs5z5xRnhefcDKh/7ZnF+87OUZE/6Fk4j2Pd2kpmd/Crse6fJadWj+fUSkaORnQN+0\nMvh827deesWcyAF981qC+tLFKEYAAAAHU0lEQVT9L06TtXVdeN4bf/TSOza2LKD7nfzPln9WRIpK\nfgX0xobgoYH+ro3tAS30e0d76aUB65lsXuXWEk+1wC+TaO4+NPXPFREJkT8vRRe9Dg+dFNwtssi3\niFXt5vif37QK6lrQl51O3zsZ9v1RtmshIgUiPwL65rXwyClei9s/q9PfOq7dEv8ez/0M6hIoF0+H\nPsnfw2/Cg3DiX8PzewxO3TNEpGjkR0AP7dYIXUrW3499xlOx7/P0eeF5J9wGnfonXpehE+KXaS7/\nkMRo5yIiCciPgF67Kfg8dFbnRt9ysW2i7KcZy077wEGXxC/nF2mxq1HXNv+558/w0j2HBF8rb+Ym\n0CIi5EtAX/ZuYuXKQlZU/OETkcsFaqwLzzvruejlAwP6D+51xwEHxX9OqMCZn6ErNAaOYxcRSVB+\nBPQZ/5NYudKQSTd7HBu53EEXe+nug7z1XIafCVcuDg62oQID+rAJ8Os10HdE9PKT3oicHzhBqLID\nDA5YYqAkvwYfiUhuyI+AnuhIkEizKIeMd5+/7ls442m4ZoX3YvPUh9xknR2+XYn6Hwhtu7rZoMPP\njPyMppD++/LW4X8Z+F2zEnYa7p3/dkNAXQM+U1ICp051SwZA4muqi4gEyI+m4PF/hg1LvNUTowkM\n6Pud747j7/PyBh7ljvtPgq4DYTffDMzDrnSt4qGnemXH3QnDz4L7jwl+RqQ+9EhrxVy1DCrbufQx\nN7rlAkoCvj8jtcIveMst7CUi0gL5EdBLShPbeScwoB//59j38wd3gLbd4Jgbwsv1OyA8zzbCpZ9G\nDuJdd3Mt8gN+Cq07efkHXuR+wHXBfDkj8ue7DXQ/IiItkB8BHWDzmvhlQvvQk2UMXPQ+bFkHU09w\nebYJOkXYz/OKRa7LxN8qj2an4cHdMCIiKZI/Af2M/4Xb94p87afvwOcvuS3X9r8g8siVluq+R/D2\ndGVRhhRqjXIRybL8Ceidq2D3MfDFS+HXeg1xPwDH3Zz6Zwf2dx/RgjHnIiIZkD8BHWDCA3BDL5ee\n+ChUHQINtbE/kwr+Fn/3QVrCVkRyVn4F9MChfoOOz9xz/TM3+0dYQ11EJEfkV0A3Bo69CQa0YE/O\nZHTZGc57HXpH6cMXEckBSU0sMsYca4z53BjzpTHm6lRVKqaRP4PewzLyqCD99oOyisw/V0QkQS0O\n6MaYUuBOYAwwGPihMUbrvoqIZEkyLfT9gS+ttYuttXXA48C41FRLRESaK5mA3gf4OuB8hS8viDFm\nkjFmtjFmdnV1dRKPExGRWNK+OJe1doq1doS1dkT37t3T/TgRkaKVTEBfCQTOge/ryxMRkSxIJqB/\nAAw0xuxsjKkAJgLaO01EJEtaPA7dWttgjPk58ApQCtxvrf0sZTUTEZFmSWpikbX2ReDFFNVFRESS\nYGzgSoLpfpgx1cCyFn68G/BNCquTD/Q7Fwf9zsUhmd95gLU27qiSjAb0ZBhjZltrY2zeWXj0OxcH\n/c7FIRO/c37sKSoiInEpoIuIFIh8CuhTsl2BLNDvXBz0OxeHtP/OedOHLiIiseVTC11ERGLIi4Ce\nlXXXs8gY088YM9MYM98Y85kx5hfZrlMmGGNKjTFzjTHTs12XTDDGdDLGPGWMWWiMWWCMOTDbdUo3\nY8xlvn/TnxpjHjPGtIr/qfxjjLnfGLPOGPNpQF4XY8xrxphFvmPnVD835wN6ka673gBcbq0dDIwE\nLiqC3xngF8CCbFcig24HXrbWDgL2osB/d2NMH+ASYIS1dghuhvnE7NYqbR4Ejg3JuxqYYa0dCMzw\nnadUzgd0inDddWvtamvth770Ztx/6GFLExcSY0xf4Hjg3mzXJROMMR2Bw4D7AKy1ddbajdmtVUaU\nAa2NMWVAG2BVluuTFtbat4D1IdnjgKm+9FTgpFQ/Nx8CekLrrhcqY0wVMBx4L7s1Sbu/Ar8CmrJd\nkQzZGagGHvB1M91rjGmb7Uqlk7V2JXArsBxYDdRYa1/Nbq0yqqe1drUvvQbomeoH5ENAL1rGmHbA\n08Cl1tpN2a5PuhhjTgDWWWvnZLsuGVQG7APcZa0dDmwlDX+C5xJfn/E43JfZTkBbY8yZ2a1Vdlg3\nvDDlQwzzIaAX5brrxphyXDB/xFr7TLbrk2YHA2ONMUtxXWqjjTEPZ7dKabcCWGGt9f/l9RQuwBey\no4Al1tpqa2098AxwUJbrlElrjTG9AXzHdal+QD4E9KJbd90YY3B9qwustX/Jdn3SzVp7jbW2r7W2\nCvf/77+ttQXdcrPWrgG+Nsbs4cs6EpifxSplwnJgpDGmje/f+JEU+IvgENOAc3zpc4DnU/2ApJbP\nzYQiXXf9YOAsYJ4x5iNf3rW+5YqlcFwMPOJrqCwGfpTl+qSVtfY9Y8xTwIe4kVxzKdAZo8aYx4BR\nQDdjzArgd8BNwJPGmPNwq86emvLnaqaoiEhhyIcuFxERSYACuohIgVBAFxEpEAroIiIFQgFdRKRA\nKKCLiBQIBXQRkQKhgC4iUiD+H9MZQ6auhjQSAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch:  100000\n",
            "Loss:  tensor(nan, dtype=torch.float64, grad_fn=<SumBackward0>)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wFNDzxfolMLkjrJgdnL9xOfz7evjsmeif3X0M7HG8S2s3IpGCpYCeL7583R0/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\nKKCLiBQIBXQRkQKhgC4iUiD+H9MZQ6auhjQSAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "tensor(nan, dtype=torch.float64, requires_grad=True)\n",
            "tensor(nan, dtype=torch.float64, requires_grad=True)\n",
            "tensor(nan, dtype=torch.float64, requires_grad=True)\n",
            "tensor(nan, dtype=torch.float64, requires_grad=True)\n",
            "tensor(nan, dtype=torch.float64, requires_grad=True)\n",
            "tensor(nan, dtype=torch.float64, requires_grad=True)\n",
            "tensor(nan, dtype=torch.float64, requires_grad=True)\n",
            "tensor(nan, dtype=torch.float64, requires_grad=True)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hUpls0GpSv3L",
        "colab_type": "code",
        "outputId": "957d0daa-9ec3-4022-a0e3-ff0c215d68d5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        }
      },
      "source": [
        "losses = np.array(losses)\n",
        "plt.plot(losses)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f525cb63128>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ljZ0fP4bz7xS",
        "colab_type": "code",
        "outputId": "967674f0-84e3-4d27-b77d-a60bc7462732",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 933
        }
      },
      "source": [
        "import torch\n",
        "from torch import nn\n",
        "from torchviz import make_dot, make_dot_from_trace\n",
        "\n",
        "x = np.array([_/100 for _ in range(1000)])\n",
        "y = 4.5*x + 3 + 2.8 * np.sin( 0.5 * pi * x + pi/3) - 5.2 * np.sin(0.25 * pi * x + pi/5) + np.random.normal(size=1000)\n",
        "\n",
        "\n",
        "x = Variable(torch.tensor(x,dtype=torch.double))\n",
        "y= Variable(torch.tensor(y,dtype=torch.double))\n",
        "\n",
        "params = [0]*8\n",
        "params[0] = m = Variable(torch.tensor(1.2,dtype=torch.double),requires_grad=True)\n",
        "params[1] = b = Variable(torch.tensor(0,dtype=torch.double),requires_grad=True)\n",
        "params[2] = A1 = Variable(torch.tensor(2.7,dtype=torch.double),requires_grad=True)\n",
        "params[3] = w1 = Variable(torch.tensor(0.45*pi,dtype=torch.double),requires_grad=True)\n",
        "params[4] = c1 = Variable(torch.tensor(1.1*pi/3,dtype=torch.double),requires_grad=True)\n",
        "params[5] = A2 = Variable(torch.tensor(-5.0,dtype=torch.double),requires_grad=True)\n",
        "params[6] = w2 = Variable(torch.tensor(0.23*pi,dtype=torch.double),requires_grad=True)\n",
        "params[7] = c2 = Variable(torch.tensor(0.9*pi/5,dtype=torch.double),requires_grad=True)\n",
        "\n",
        "# Compute the function\n",
        "Y = params[0]*x+params[1]+params[2]*torch.sin(params[3]*x+params[4])+params[5]*torch.sin(params[6]*x+params[7])\n",
        "\n",
        "# Compute the loss\n",
        "loss = ((Y-y)*(Y-y))/2\n",
        "loss = loss.sum()\n",
        "\n",
        "make_dot(loss)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f525714af60>"
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